The question is from the following:
Convex Optimization Algorithm (p.512)----- Prof. Bertsekas
Let $f: R^n \rightarrow (-\infty, \infty]$ be a proper convex function. For every $x \in \text{ri}(\text{dom}(f)) $,
$$\partial f(x) = S^{\perp}+G$$
Notation:
1. $\partial f(x)$ is the set of all subgradients of $f$ at $x$.
2. $S$: the subspace that is parallel to the affine hull of dom$(f).$
3. $G$ is a nonempty convex and compact set.
4. $\text{ri}()$: relative interior of (a set)
I have no ideat of what this proposition is talking about. How to prove it?